Solutions and Answers to Pythagoras' Theorem Problems

This final page provides detailed solutions to the problems presented earlier, serving as a valuable resource for students seeking Pythagoras Theorem questions for Class 8 PDF or similar study materials.

For the problem with sides 19 and 37.2:

1. 19² = 361
2. 37.2² = 1383.84
3. 361 + 1383.84 = 1744.84
4. √1744.84 ≈ 41.8 Therefore, c² = 41.8

For the problem with sides 3 and 5:

1. 3² = 9
2. 5² = 25
3. 25 + 9 = 34
4. √34 ≈ 5.8 Therefore, c² = 5.8

For the problem with sides 7 and 12:

1. 7² = 49
2. 12² = 144
3. 144 + 49 = 193
4. √193 ≈ 13.9 Therefore, c² = 13.9

Highlight: Always show your work step-by-step when solving Pythagoras' Theorem problems. This helps in identifying any potential errors and demonstrates your understanding of the process.

These solutions provide a comprehensive guide for students to check their work and understand the correct approach to solving various types of Pythagoras' Theorem problems. They serve as excellent practice for pythagoras' theorem questions with answers and can be used to reinforce learning and problem-solving skills.

Understanding Pythagoras' Theorem

Pythagoras' Theorem is a cornerstone of Euclidean geometry, establishing a crucial relationship between the sides of a right-angled triangle. This theorem is essential for GCSE mathematics and forms the basis for many advanced geometric concepts.

Definition: Pythagoras' Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of squares of the lengths of the other two sides.

The theorem is typically expressed using the formula:

a² + b² = c²

Where:

• c represents the length of the hypotenuse
• a and b represent the lengths of the other two sides

Highlight: The hypotenuse is always the longest side of a right-angled triangle and is opposite the right angle.

It's important to note that while the guide uses a, b, and c to denote the sides, these letters may vary in different problems. Some questions might use x, y, and z, or other letters to represent the sides of the triangle.

Vocabulary: Hypotenuse - The longest side of a right-angled triangle, opposite the right angle.

This fundamental theorem provides a powerful tool for solving various geometric problems, including finding missing sides of right-angled triangles and verifying if a triangle is indeed right-angled.